We studied the Kane-Mele-Hubbard model at half filling with Zeeman magnetic field using rotationally invariant slave boson method. The competition between external magnetic field and spin orbital coupling at large Hubbard U is explored. It is found that different canted antiferromagnetic phases exist in the presence of longitudinal and transverse magnetic fields. With longitudinal external magnetic field and strong electron correlation, the z component of the local moment is preferred by the finite spin-orbital coupling.We studied the Kane-Mele-Hubbard model at half filling with Zeeman magnetic field using rotationally invariant slave boson method. The competition between external magnetic field and spin orbital coupling at large Hubbard U is explored. It is found that different canted antiferromagnetic phases exist in the presence of longitudinal and transverse magnetic fields. With longitudinal external magnetic field and strong electron correlation, the z component of the local moment is preferred by the finite spin-orbital coupling.

Journal of Physics Conference SeriesMay 17, 20171 citation

The 1d Hubbard Model

WORLD SCIENTIFIC eBooksMar 1, 20080 citations

Zeeman field induced corner states in the Kane-Mele-Hubbard model

Jie Zhang, Han Xu, Yu Wang

We investigate how the in-plane Zeeman field and the Hubbard interaction can jointly affect the topological states in the Kane-Mele-Hubbard model. At low Zeeman field, the projector quantum Monte Carlo (PQMC) simulations demonstrate Mott transitions between the higher-order topological insulator induced by the in-plane Zeeman field and the antiferromagnetic insulator induced by the Hubbard interaction. The interacting higher-order topological state on a finite-sized honeycomb lattice is characterized by the local density of states derived from the real-space spectral function. In the higher-order topological phase, the mirror-symmetry protected corner states exist on the diamond-shaped honeycomb lattice. In terms of spatial extent of corner states induced by the in-plane Zeeman field in the Kane-Mele and Kane-Mele-Hubbard models, we show that the effect of the Hubbard interaction is to contribute some extra in-plane Zeeman field. At the mean-field level, we characterize the bulk topology by the mirror winding number and calculate the full phase diagram of the Kane-Mele-Hubbard model under the influence of the in-plane Zeeman field. The mean-field phase diagram shows that a high in-plane Zeeman field drives the system into a spin-polarized (topologically trivial) phase. In particular, the upper limit of the Zeeman field that can induce corner states in the Kane-Mele model is found to be ${h}_{c}=1.0$ . In the parameter region of PQMC simulations, the mean-field solutions qualitatively agree with the PQMC results.We investigate how the in-plane Zeeman field and the Hubbard interaction can jointly affect the topological states in the Kane-Mele-Hubbard model. At low Zeeman field, the projector quantum Monte Carlo (PQMC) simulations demonstrate Mott transitions between the higher-order topological insulator induced by the in-plane Zeeman field and the antiferromagnetic insulator induced by the Hubbard interaction. The interacting higher-order topological state on a finite-sized honeycomb lattice is characterized by the local density of states derived from the real-space spectral function. In the higher-order topological phase, the mirror-symmetry protected corner states exist on the diamond-shaped honeycomb lattice. In terms of spatial extent of corner states induced by the in-plane Zeeman field in the Kane-Mele and Kane-Mele-Hubbard models, we show that the effect of the Hubbard interaction is to contribute some extra in-plane Zeeman field. At the mean-field level, we characterize the bulk topology by the mirror winding number and calculate the full phase diagram of the Kane-Mele-Hubbard model under the influence of the in-plane Zeeman field. The mean-field phase diagram shows that a high in-plane Zeeman field drives the system into a spin-polarized (topologically trivial) phase. In particular, the upper limit of the Zeeman field that can induce corner states in the Kane-Mele model is found to be ${h}_{c}=1.0$. In the parameter region of PQMC simulations, the mean-field solutions qualitatively agree with the PQMC results.

arXiv:2408.09492Physical review. B./Physical review. BJan 6, 20251 citation

Quantum phase transitions in the Kane-Mele-Hubbard model

Martin Hohenadler, Zi Yang Meng, Thomas C. Lang +3 more

We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard $U$ is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard $U$ is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.

arXiv:1111.3949Physical Review BMar 29, 2012159 citations

{h}_{c}=1.0

. In the parameter region of PQMC simulations, the mean-field solutions qualitatively agree with the PQMC results.

U

is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.